Data.Semigroup.Additive

Documentation

(+) :: (Additive - Semigroup) a => a -> a -> a infixl 6

(-) :: (Additive - Group) a => a -> a -> a infixl 6

zero :: (Additive - Monoid) a => a

newtype Additive a

A commutative Semigroup under +.

Constructors

Additive

Fields

• unAdditive :: a

Instances

Functor Additive

Defined in Data.Semigroup.Additive

Methods

fmap :: (a -> b) -> Additive a -> Additive b

(<$) :: a -> Additive b -> Additive a

Applicative Additive

Defined in Data.Semigroup.Additive

Methods

pure :: a -> Additive a

(<*>) :: Additive (a -> b) -> Additive a -> Additive b

liftA2 :: (a -> b -> c) -> Additive a -> Additive b -> Additive c

(*>) :: Additive a -> Additive b -> Additive b

(<*) :: Additive a -> Additive b -> Additive a

Distributive Additive

Defined in Data.Semigroup.Additive

Methods

distribute :: Functor f => f (Additive a) -> Additive (f a)

collect :: Functor f => (a -> Additive b) -> f a -> Additive (f b)

distributeM :: Monad m => m (Additive a) -> Additive (m a)

collectM :: Monad m => (a -> Additive b) -> m a -> Additive (m b)

Representable Additive

Defined in Data.Semigroup.Additive

Associated Types

type Rep Additive :: Type

Methods

tabulate :: (Rep Additive -> a) -> Additive a

index :: Additive a -> Rep Additive -> a

Semiring Bool => Semimodule Bool (Additive Bool)

Defined in Data.Semimodule

Methods

(*.) :: Bool -> Additive Bool -> Additive Bool

(.*) :: Additive Bool -> Bool -> Additive Bool

Semiring Double => Semimodule Double (Additive Double)

Defined in Data.Semimodule

Methods

(*.) :: Double -> Additive Double -> Additive Double

(.*) :: Additive Double -> Double -> Additive Double

Semiring Float => Semimodule Float (Additive Float)

Defined in Data.Semimodule

Methods

(*.) :: Float -> Additive Float -> Additive Float

(.*) :: Additive Float -> Float -> Additive Float

Semiring Int => Semimodule Int (Additive Int)

Defined in Data.Semimodule

Methods

(*.) :: Int -> Additive Int -> Additive Int

(.*) :: Additive Int -> Int -> Additive Int

Semiring Int8 => Semimodule Int8 (Additive Int8)

Defined in Data.Semimodule

Methods

(*.) :: Int8 -> Additive Int8 -> Additive Int8

(.*) :: Additive Int8 -> Int8 -> Additive Int8

Semiring Int16 => Semimodule Int16 (Additive Int16)

Defined in Data.Semimodule

Methods

(*.) :: Int16 -> Additive Int16 -> Additive Int16

(.*) :: Additive Int16 -> Int16 -> Additive Int16

Semiring Int32 => Semimodule Int32 (Additive Int32)

Defined in Data.Semimodule

Methods

(*.) :: Int32 -> Additive Int32 -> Additive Int32

(.*) :: Additive Int32 -> Int32 -> Additive Int32

Semiring Int64 => Semimodule Int64 (Additive Int64)

Defined in Data.Semimodule

Methods

(*.) :: Int64 -> Additive Int64 -> Additive Int64

(.*) :: Additive Int64 -> Int64 -> Additive Int64

Semiring Word => Semimodule Word (Additive Word)

Defined in Data.Semimodule

Methods

(*.) :: Word -> Additive Word -> Additive Word

(.*) :: Additive Word -> Word -> Additive Word

Semiring Word8 => Semimodule Word8 (Additive Word8)

Defined in Data.Semimodule

Methods

(*.) :: Word8 -> Additive Word8 -> Additive Word8

(.*) :: Additive Word8 -> Word8 -> Additive Word8

Semiring Word16 => Semimodule Word16 (Additive Word16)

Defined in Data.Semimodule

Methods

(*.) :: Word16 -> Additive Word16 -> Additive Word16

(.*) :: Additive Word16 -> Word16 -> Additive Word16

Semiring Word32 => Semimodule Word32 (Additive Word32)

Defined in Data.Semimodule

Methods

(*.) :: Word32 -> Additive Word32 -> Additive Word32

(.*) :: Additive Word32 -> Word32 -> Additive Word32

Semiring Word64 => Semimodule Word64 (Additive Word64)

Defined in Data.Semimodule

Methods

(*.) :: Word64 -> Additive Word64 -> Additive Word64

(.*) :: Additive Word64 -> Word64 -> Additive Word64

(Ring a, Semimodule r a) => Semimodule r (Additive (Complex a))

Defined in Data.Semimodule

Methods

(*.) :: r -> Additive (Complex a) -> Additive (Complex a)

(.*) :: Additive (Complex a) -> r -> Additive (Complex a)

(Semiring a, Semimodule r a) => Semimodule r (Additive (Ratio a))

Defined in Data.Semimodule

Methods

(*.) :: r -> Additive (Ratio a) -> Additive (Ratio a)

(.*) :: Additive (Ratio a) -> r -> Additive (Ratio a)

Semiring Uni => Semimodule Uni (Additive Uni)

Defined in Data.Semimodule

Methods

(*.) :: Uni -> Additive Uni -> Additive Uni

(.*) :: Additive Uni -> Uni -> Additive Uni

Semiring Deci => Semimodule Deci (Additive Deci)

Defined in Data.Semimodule

Methods

(*.) :: Deci -> Additive Deci -> Additive Deci

(.*) :: Additive Deci -> Deci -> Additive Deci

Semiring Centi => Semimodule Centi (Additive Centi)

Defined in Data.Semimodule

Methods

(*.) :: Centi -> Additive Centi -> Additive Centi

(.*) :: Additive Centi -> Centi -> Additive Centi

Semiring Milli => Semimodule Milli (Additive Milli)

Defined in Data.Semimodule

Methods

(*.) :: Milli -> Additive Milli -> Additive Milli

(.*) :: Additive Milli -> Milli -> Additive Milli

Semiring Micro => Semimodule Micro (Additive Micro)

Defined in Data.Semimodule

Methods

(*.) :: Micro -> Additive Micro -> Additive Micro

(.*) :: Additive Micro -> Micro -> Additive Micro

Semiring Nano => Semimodule Nano (Additive Nano)

Defined in Data.Semimodule

Methods

(*.) :: Nano -> Additive Nano -> Additive Nano

(.*) :: Additive Nano -> Nano -> Additive Nano

Semiring Pico => Semimodule Pico (Additive Pico)

Defined in Data.Semimodule

Methods

(*.) :: Pico -> Additive Pico -> Additive Pico

(.*) :: Additive Pico -> Pico -> Additive Pico

Semiring CFloat => Semimodule CFloat (Additive CFloat)

Defined in Data.Semimodule

Methods

(*.) :: CFloat -> Additive CFloat -> Additive CFloat

(.*) :: Additive CFloat -> CFloat -> Additive CFloat

Semiring CDouble => Semimodule CDouble (Additive CDouble)

Defined in Data.Semimodule

Methods

(*.) :: CDouble -> Additive CDouble -> Additive CDouble

(.*) :: Additive CDouble -> CDouble -> Additive CDouble

Eq a => Eq (Additive a)

Defined in Data.Semigroup.Additive

Methods

(==) :: Additive a -> Additive a -> Bool

(/=) :: Additive a -> Additive a -> Bool

Ord a => Ord (Additive a)

Defined in Data.Semigroup.Additive

Methods

compare :: Additive a -> Additive a -> Ordering

(<) :: Additive a -> Additive a -> Bool

(<=) :: Additive a -> Additive a -> Bool

(>) :: Additive a -> Additive a -> Bool

(>=) :: Additive a -> Additive a -> Bool

max :: Additive a -> Additive a -> Additive a

min :: Additive a -> Additive a -> Additive a

Show a => Show (Additive a)

Defined in Data.Semigroup.Additive

Methods

showsPrec :: Int -> Additive a -> ShowS

show :: Additive a -> String

showList :: [Additive a] -> ShowS

Generic (Additive a)

Defined in Data.Semigroup.Additive

Associated Types

type Rep (Additive a) :: Type -> Type

Methods

from :: Additive a -> Rep (Additive a) x

to :: Rep (Additive a) x -> Additive a

Semigroup (Additive Bool)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Bool -> Additive Bool -> Additive Bool

sconcat :: NonEmpty (Additive Bool) -> Additive Bool

stimes :: Integral b => b -> Additive Bool -> Additive Bool

Semigroup (Additive Double)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Double -> Additive Double -> Additive Double

sconcat :: NonEmpty (Additive Double) -> Additive Double

stimes :: Integral b => b -> Additive Double -> Additive Double

Semigroup (Additive Float)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Float -> Additive Float -> Additive Float

sconcat :: NonEmpty (Additive Float) -> Additive Float

stimes :: Integral b => b -> Additive Float -> Additive Float

(Additive - Semigroup) b => Semigroup (Additive (a -> b))

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive (a -> b) -> Additive (a -> b) -> Additive (a -> b)

sconcat :: NonEmpty (Additive (a -> b)) -> Additive (a -> b)

stimes :: Integral b0 => b0 -> Additive (a -> b) -> Additive (a -> b)

Semigroup (Additive Int)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Int -> Additive Int -> Additive Int

sconcat :: NonEmpty (Additive Int) -> Additive Int

stimes :: Integral b => b -> Additive Int -> Additive Int

Semigroup (Additive Int8)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Int8 -> Additive Int8 -> Additive Int8

sconcat :: NonEmpty (Additive Int8) -> Additive Int8

stimes :: Integral b => b -> Additive Int8 -> Additive Int8

Semigroup (Additive Int16)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Int16 -> Additive Int16 -> Additive Int16

sconcat :: NonEmpty (Additive Int16) -> Additive Int16

stimes :: Integral b => b -> Additive Int16 -> Additive Int16

Semigroup (Additive Int32)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Int32 -> Additive Int32 -> Additive Int32

sconcat :: NonEmpty (Additive Int32) -> Additive Int32

stimes :: Integral b => b -> Additive Int32 -> Additive Int32

Semigroup (Additive Int64)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Int64 -> Additive Int64 -> Additive Int64

sconcat :: NonEmpty (Additive Int64) -> Additive Int64

stimes :: Integral b => b -> Additive Int64 -> Additive Int64

Semigroup (Additive Integer)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Integer -> Additive Integer -> Additive Integer

sconcat :: NonEmpty (Additive Integer) -> Additive Integer

stimes :: Integral b => b -> Additive Integer -> Additive Integer

Semigroup (Additive Natural)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Natural -> Additive Natural -> Additive Natural

sconcat :: NonEmpty (Additive Natural) -> Additive Natural

stimes :: Integral b => b -> Additive Natural -> Additive Natural

Semigroup (Additive [a])

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive [a] -> Additive [a] -> Additive [a]

sconcat :: NonEmpty (Additive [a]) -> Additive [a]

stimes :: Integral b => b -> Additive [a] -> Additive [a]

(Additive - Semigroup) a => Semigroup (Additive (Maybe a))

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive (Maybe a) -> Additive (Maybe a) -> Additive (Maybe a)

sconcat :: NonEmpty (Additive (Maybe a)) -> Additive (Maybe a)

stimes :: Integral b => b -> Additive (Maybe a) -> Additive (Maybe a)

((Additive - Semigroup) a, (Multiplicative - Semigroup) a) => Semigroup (Additive (Ratio a))

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive (Ratio a) -> Additive (Ratio a) -> Additive (Ratio a)

sconcat :: NonEmpty (Additive (Ratio a)) -> Additive (Ratio a)

stimes :: Integral b => b -> Additive (Ratio a) -> Additive (Ratio a)

Semigroup (Additive Word)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Word -> Additive Word -> Additive Word

sconcat :: NonEmpty (Additive Word) -> Additive Word

stimes :: Integral b => b -> Additive Word -> Additive Word

Semigroup (Additive Word8)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Word8 -> Additive Word8 -> Additive Word8

sconcat :: NonEmpty (Additive Word8) -> Additive Word8

stimes :: Integral b => b -> Additive Word8 -> Additive Word8

Semigroup (Additive Word16)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Word16 -> Additive Word16 -> Additive Word16

sconcat :: NonEmpty (Additive Word16) -> Additive Word16

stimes :: Integral b => b -> Additive Word16 -> Additive Word16

Semigroup (Additive Word32)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Word32 -> Additive Word32 -> Additive Word32

sconcat :: NonEmpty (Additive Word32) -> Additive Word32

stimes :: Integral b => b -> Additive Word32 -> Additive Word32

Semigroup (Additive Word64)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Word64 -> Additive Word64 -> Additive Word64

sconcat :: NonEmpty (Additive Word64) -> Additive Word64

stimes :: Integral b => b -> Additive Word64 -> Additive Word64

((Additive - Semigroup) a, (Additive - Semigroup) b) => Semigroup (Additive (Either a b))

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive (Either a b) -> Additive (Either a b) -> Additive (Either a b)

sconcat :: NonEmpty (Additive (Either a b)) -> Additive (Either a b)

stimes :: Integral b0 => b0 -> Additive (Either a b) -> Additive (Either a b)

Semigroup (Additive ())

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive () -> Additive () -> Additive ()

sconcat :: NonEmpty (Additive ()) -> Additive ()

stimes :: Integral b => b -> Additive () -> Additive ()

((Additive - Semigroup) a, (Additive - Semigroup) b) => Semigroup (Additive (a, b))

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive (a, b) -> Additive (a, b) -> Additive (a, b)

sconcat :: NonEmpty (Additive (a, b)) -> Additive (a, b)

stimes :: Integral b0 => b0 -> Additive (a, b) -> Additive (a, b)

(Additive - Semigroup) a => Semigroup (Additive (Complex a))

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive (Complex a) -> Additive (Complex a) -> Additive (Complex a)

sconcat :: NonEmpty (Additive (Complex a)) -> Additive (Complex a)

stimes :: Integral b => b -> Additive (Complex a) -> Additive (Complex a)

Semigroup (Additive Uni)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Uni -> Additive Uni -> Additive Uni

sconcat :: NonEmpty (Additive Uni) -> Additive Uni

stimes :: Integral b => b -> Additive Uni -> Additive Uni

Semigroup (Additive Deci)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Deci -> Additive Deci -> Additive Deci

sconcat :: NonEmpty (Additive Deci) -> Additive Deci

stimes :: Integral b => b -> Additive Deci -> Additive Deci

Semigroup (Additive Centi)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Centi -> Additive Centi -> Additive Centi

sconcat :: NonEmpty (Additive Centi) -> Additive Centi

stimes :: Integral b => b -> Additive Centi -> Additive Centi

Semigroup (Additive Milli)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Milli -> Additive Milli -> Additive Milli

sconcat :: NonEmpty (Additive Milli) -> Additive Milli

stimes :: Integral b => b -> Additive Milli -> Additive Milli

Semigroup (Additive Micro)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Micro -> Additive Micro -> Additive Micro

sconcat :: NonEmpty (Additive Micro) -> Additive Micro

stimes :: Integral b => b -> Additive Micro -> Additive Micro

Semigroup (Additive Nano)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Nano -> Additive Nano -> Additive Nano

sconcat :: NonEmpty (Additive Nano) -> Additive Nano

stimes :: Integral b => b -> Additive Nano -> Additive Nano

Semigroup (Additive Pico)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive Pico -> Additive Pico -> Additive Pico

sconcat :: NonEmpty (Additive Pico) -> Additive Pico

stimes :: Integral b => b -> Additive Pico -> Additive Pico

(Additive - Semigroup) a => Semigroup (Additive (Down a))

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive (Down a) -> Additive (Down a) -> Additive (Down a)

sconcat :: NonEmpty (Additive (Down a)) -> Additive (Down a)

stimes :: Integral b => b -> Additive (Down a) -> Additive (Down a)

Semigroup (Additive CFloat)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive CFloat -> Additive CFloat -> Additive CFloat

sconcat :: NonEmpty (Additive CFloat) -> Additive CFloat

stimes :: Integral b => b -> Additive CFloat -> Additive CFloat

Semigroup (Additive CDouble)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive CDouble -> Additive CDouble -> Additive CDouble

sconcat :: NonEmpty (Additive CDouble) -> Additive CDouble

stimes :: Integral b => b -> Additive CDouble -> Additive CDouble

Semigroup (Additive (NonEmpty a))

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive (NonEmpty a) -> Additive (NonEmpty a) -> Additive (NonEmpty a)

sconcat :: NonEmpty (Additive (NonEmpty a)) -> Additive (NonEmpty a)

stimes :: Integral b => b -> Additive (NonEmpty a) -> Additive (NonEmpty a)

(Additive - Semigroup) a => Semigroup (Additive (IntMap a))

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive (IntMap a) -> Additive (IntMap a) -> Additive (IntMap a)

sconcat :: NonEmpty (Additive (IntMap a)) -> Additive (IntMap a)

stimes :: Integral b => b -> Additive (IntMap a) -> Additive (IntMap a)

Semigroup (Additive IntSet)

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive IntSet -> Additive IntSet -> Additive IntSet

sconcat :: NonEmpty (Additive IntSet) -> Additive IntSet

stimes :: Integral b => b -> Additive IntSet -> Additive IntSet

(Ord k, (Additive - Semigroup) a) => Semigroup (Additive (Map k a))

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive (Map k a) -> Additive (Map k a) -> Additive (Map k a)

sconcat :: NonEmpty (Additive (Map k a)) -> Additive (Map k a)

stimes :: Integral b => b -> Additive (Map k a) -> Additive (Map k a)

Ord a => Semigroup (Additive (Set a))

Defined in Data.Semigroup.Additive

Methods

(<>) :: Additive (Set a) -> Additive (Set a) -> Additive (Set a)

sconcat :: NonEmpty (Additive (Set a)) -> Additive (Set a)

stimes :: Integral b => b -> Additive (Set a) -> Additive (Set a)

(Additive - Semigroup) a => Semigroup (Additive (V4 a))

Matrix addition.

>>> m24 1 2 3 4 5 6 7 8 <> m24 1 2 3 4 5 6 7 8 :: M24 Int
V2 (V4 2 4 6 8) (V4 10 12 14 16)

Defined in Data.Semimodule.Vector

Methods

(<>) :: Additive (V4 a) -> Additive (V4 a) -> Additive (V4 a)

sconcat :: NonEmpty (Additive (V4 a)) -> Additive (V4 a)

stimes :: Integral b => b -> Additive (V4 a) -> Additive (V4 a)

Semigroup (Additive I3)

Defined in Data.Semimodule.Vector

Methods

(<>) :: Additive I3 -> Additive I3 -> Additive I3

sconcat :: NonEmpty (Additive I3) -> Additive I3

stimes :: Integral b => b -> Additive I3 -> Additive I3

(Additive - Semigroup) a => Semigroup (Additive (V3 a))

Matrix addition.

>>> V2 (V3 1 2 3) (V3 4 5 6) <> V2 (V3 7 8 9) (V3 1 2 3)
V2 (V3 8 10 12) (V3 5 7 9)

Defined in Data.Semimodule.Vector

Methods

(<>) :: Additive (V3 a) -> Additive (V3 a) -> Additive (V3 a)

sconcat :: NonEmpty (Additive (V3 a)) -> Additive (V3 a)

stimes :: Integral b => b -> Additive (V3 a) -> Additive (V3 a)

Semigroup (Additive I2)

Defined in Data.Semimodule.Vector

Methods

(<>) :: Additive I2 -> Additive I2 -> Additive I2

sconcat :: NonEmpty (Additive I2) -> Additive I2

stimes :: Integral b => b -> Additive I2 -> Additive I2

(Additive - Semigroup) a => Semigroup (Additive (V2 a))

Matrix addition.

>>> m23 1 2 3 4 5 6 <> m23 7 8 9 1 2 3 :: M23 Int
V2 (V3 8 10 12) (V3 5 7 9)

Defined in Data.Semimodule.Vector

Methods

(<>) :: Additive (V2 a) -> Additive (V2 a) -> Additive (V2 a)

sconcat :: NonEmpty (Additive (V2 a)) -> Additive (V2 a)

stimes :: Integral b => b -> Additive (V2 a) -> Additive (V2 a)

(Additive - Semigroup) a => Semigroup (Additive (Quaternion a))

Defined in Data.Algebra.Quaternion

Methods

(<>) :: Additive (Quaternion a) -> Additive (Quaternion a) -> Additive (Quaternion a)

sconcat :: NonEmpty (Additive (Quaternion a)) -> Additive (Quaternion a)

stimes :: Integral b => b -> Additive (Quaternion a) -> Additive (Quaternion a)

Monoid (Additive Bool)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Bool

mappend :: Additive Bool -> Additive Bool -> Additive Bool

mconcat :: [Additive Bool] -> Additive Bool

Monoid (Additive Double)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Double

mappend :: Additive Double -> Additive Double -> Additive Double

mconcat :: [Additive Double] -> Additive Double

Monoid (Additive Float)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Float

mappend :: Additive Float -> Additive Float -> Additive Float

mconcat :: [Additive Float] -> Additive Float

(Additive - Monoid) b => Monoid (Additive (a -> b))

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive (a -> b)

mappend :: Additive (a -> b) -> Additive (a -> b) -> Additive (a -> b)

mconcat :: [Additive (a -> b)] -> Additive (a -> b)

Monoid (Additive Int)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Int

mappend :: Additive Int -> Additive Int -> Additive Int

mconcat :: [Additive Int] -> Additive Int

Monoid (Additive Int8)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Int8

mappend :: Additive Int8 -> Additive Int8 -> Additive Int8

mconcat :: [Additive Int8] -> Additive Int8

Monoid (Additive Int16)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Int16

mappend :: Additive Int16 -> Additive Int16 -> Additive Int16

mconcat :: [Additive Int16] -> Additive Int16

Monoid (Additive Int32)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Int32

mappend :: Additive Int32 -> Additive Int32 -> Additive Int32

mconcat :: [Additive Int32] -> Additive Int32

Monoid (Additive Int64)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Int64

mappend :: Additive Int64 -> Additive Int64 -> Additive Int64

mconcat :: [Additive Int64] -> Additive Int64

Monoid (Additive Integer)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Integer

mappend :: Additive Integer -> Additive Integer -> Additive Integer

mconcat :: [Additive Integer] -> Additive Integer

Monoid (Additive Natural)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Natural

mappend :: Additive Natural -> Additive Natural -> Additive Natural

mconcat :: [Additive Natural] -> Additive Natural

Monoid (Additive [a])

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive [a]

mappend :: Additive [a] -> Additive [a] -> Additive [a]

mconcat :: [Additive [a]] -> Additive [a]

(Additive - Semigroup) a => Monoid (Additive (Maybe a))

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive (Maybe a)

mappend :: Additive (Maybe a) -> Additive (Maybe a) -> Additive (Maybe a)

mconcat :: [Additive (Maybe a)] -> Additive (Maybe a)

((Additive - Monoid) a, (Multiplicative - Monoid) a) => Monoid (Additive (Ratio a))

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive (Ratio a)

mappend :: Additive (Ratio a) -> Additive (Ratio a) -> Additive (Ratio a)

mconcat :: [Additive (Ratio a)] -> Additive (Ratio a)

Monoid (Additive Word)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Word

mappend :: Additive Word -> Additive Word -> Additive Word

mconcat :: [Additive Word] -> Additive Word

Monoid (Additive Word8)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Word8

mappend :: Additive Word8 -> Additive Word8 -> Additive Word8

mconcat :: [Additive Word8] -> Additive Word8

Monoid (Additive Word16)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Word16

mappend :: Additive Word16 -> Additive Word16 -> Additive Word16

mconcat :: [Additive Word16] -> Additive Word16

Monoid (Additive Word32)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Word32

mappend :: Additive Word32 -> Additive Word32 -> Additive Word32

mconcat :: [Additive Word32] -> Additive Word32

Monoid (Additive Word64)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Word64

mappend :: Additive Word64 -> Additive Word64 -> Additive Word64

mconcat :: [Additive Word64] -> Additive Word64

Monoid (Additive ())

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive ()

mappend :: Additive () -> Additive () -> Additive ()

mconcat :: [Additive ()] -> Additive ()

(Additive - Monoid) a => Monoid (Additive (Complex a))

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive (Complex a)

mappend :: Additive (Complex a) -> Additive (Complex a) -> Additive (Complex a)

mconcat :: [Additive (Complex a)] -> Additive (Complex a)

Monoid (Additive Uni)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Uni

mappend :: Additive Uni -> Additive Uni -> Additive Uni

mconcat :: [Additive Uni] -> Additive Uni

Monoid (Additive Deci)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Deci

mappend :: Additive Deci -> Additive Deci -> Additive Deci

mconcat :: [Additive Deci] -> Additive Deci

Monoid (Additive Centi)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Centi

mappend :: Additive Centi -> Additive Centi -> Additive Centi

mconcat :: [Additive Centi] -> Additive Centi

Monoid (Additive Milli)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Milli

mappend :: Additive Milli -> Additive Milli -> Additive Milli

mconcat :: [Additive Milli] -> Additive Milli

Monoid (Additive Micro)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Micro

mappend :: Additive Micro -> Additive Micro -> Additive Micro

mconcat :: [Additive Micro] -> Additive Micro

Monoid (Additive Nano)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Nano

mappend :: Additive Nano -> Additive Nano -> Additive Nano

mconcat :: [Additive Nano] -> Additive Nano

Monoid (Additive Pico)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive Pico

mappend :: Additive Pico -> Additive Pico -> Additive Pico

mconcat :: [Additive Pico] -> Additive Pico

(Additive - Monoid) a => Monoid (Additive (Down a))

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive (Down a)

mappend :: Additive (Down a) -> Additive (Down a) -> Additive (Down a)

mconcat :: [Additive (Down a)] -> Additive (Down a)

Monoid (Additive CFloat)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive CFloat

mappend :: Additive CFloat -> Additive CFloat -> Additive CFloat

mconcat :: [Additive CFloat] -> Additive CFloat

Monoid (Additive CDouble)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive CDouble

mappend :: Additive CDouble -> Additive CDouble -> Additive CDouble

mconcat :: [Additive CDouble] -> Additive CDouble

(Additive - Semigroup) a => Monoid (Additive (IntMap a))

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive (IntMap a)

mappend :: Additive (IntMap a) -> Additive (IntMap a) -> Additive (IntMap a)

mconcat :: [Additive (IntMap a)] -> Additive (IntMap a)

Monoid (Additive IntSet)

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive IntSet

mappend :: Additive IntSet -> Additive IntSet -> Additive IntSet

mconcat :: [Additive IntSet] -> Additive IntSet

(Ord k, (Additive - Semigroup) a) => Monoid (Additive (Map k a))

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive (Map k a)

mappend :: Additive (Map k a) -> Additive (Map k a) -> Additive (Map k a)

mconcat :: [Additive (Map k a)] -> Additive (Map k a)

Ord a => Monoid (Additive (Set a))

Defined in Data.Semigroup.Additive

Methods

mempty :: Additive (Set a)

mappend :: Additive (Set a) -> Additive (Set a) -> Additive (Set a)

mconcat :: [Additive (Set a)] -> Additive (Set a)

(Additive - Monoid) a => Monoid (Additive (V4 a))

Defined in Data.Semimodule.Vector

Methods

mempty :: Additive (V4 a)

mappend :: Additive (V4 a) -> Additive (V4 a) -> Additive (V4 a)

mconcat :: [Additive (V4 a)] -> Additive (V4 a)

Monoid (Additive I3)

Defined in Data.Semimodule.Vector

Methods

mempty :: Additive I3

mappend :: Additive I3 -> Additive I3 -> Additive I3

mconcat :: [Additive I3] -> Additive I3

(Additive - Monoid) a => Monoid (Additive (V3 a))

Defined in Data.Semimodule.Vector

Methods

mempty :: Additive (V3 a)

mappend :: Additive (V3 a) -> Additive (V3 a) -> Additive (V3 a)

mconcat :: [Additive (V3 a)] -> Additive (V3 a)

Monoid (Additive I2)

Defined in Data.Semimodule.Vector

Methods

mempty :: Additive I2

mappend :: Additive I2 -> Additive I2 -> Additive I2

mconcat :: [Additive I2] -> Additive I2

(Additive - Monoid) a => Monoid (Additive (V2 a))

Defined in Data.Semimodule.Vector

Methods

mempty :: Additive (V2 a)

mappend :: Additive (V2 a) -> Additive (V2 a) -> Additive (V2 a)

mconcat :: [Additive (V2 a)] -> Additive (V2 a)

(Additive - Monoid) a => Monoid (Additive (Quaternion a))

Defined in Data.Algebra.Quaternion

Methods

mempty :: Additive (Quaternion a)

mappend :: Additive (Quaternion a) -> Additive (Quaternion a) -> Additive (Quaternion a)

mconcat :: [Additive (Quaternion a)] -> Additive (Quaternion a)

Group (Additive Double)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Double -> Additive Double

greplicate :: Integer -> Additive Double -> Additive Double

Group (Additive Float)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Float -> Additive Float

greplicate :: Integer -> Additive Float -> Additive Float

Group (Additive Int)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Int -> Additive Int

greplicate :: Integer -> Additive Int -> Additive Int

Group (Additive Int8)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Int8 -> Additive Int8

greplicate :: Integer -> Additive Int8 -> Additive Int8

Group (Additive Int16)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Int16 -> Additive Int16

greplicate :: Integer -> Additive Int16 -> Additive Int16

Group (Additive Int32)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Int32 -> Additive Int32

greplicate :: Integer -> Additive Int32 -> Additive Int32

Group (Additive Int64)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Int64 -> Additive Int64

greplicate :: Integer -> Additive Int64 -> Additive Int64

Group (Additive Integer)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Integer -> Additive Integer

greplicate :: Integer -> Additive Integer -> Additive Integer

((Additive - Group) a, (Multiplicative - Monoid) a) => Group (Additive (Ratio a))

Defined in Data.Semigroup.Additive

Methods

inv :: Additive (Ratio a) -> Additive (Ratio a)

greplicate :: Integer -> Additive (Ratio a) -> Additive (Ratio a)

Group (Additive ())

Defined in Data.Semigroup.Additive

Methods

inv :: Additive () -> Additive ()

greplicate :: Integer -> Additive () -> Additive ()

(Additive - Group) a => Group (Additive (Complex a))

Defined in Data.Semigroup.Additive

Methods

inv :: Additive (Complex a) -> Additive (Complex a)

greplicate :: Integer -> Additive (Complex a) -> Additive (Complex a)

Group (Additive Uni)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Uni -> Additive Uni

greplicate :: Integer -> Additive Uni -> Additive Uni

Group (Additive Deci)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Deci -> Additive Deci

greplicate :: Integer -> Additive Deci -> Additive Deci

Group (Additive Centi)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Centi -> Additive Centi

greplicate :: Integer -> Additive Centi -> Additive Centi

Group (Additive Milli)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Milli -> Additive Milli

greplicate :: Integer -> Additive Milli -> Additive Milli

Group (Additive Micro)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Micro -> Additive Micro

greplicate :: Integer -> Additive Micro -> Additive Micro

Group (Additive Nano)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Nano -> Additive Nano

greplicate :: Integer -> Additive Nano -> Additive Nano

Group (Additive Pico)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive Pico -> Additive Pico

greplicate :: Integer -> Additive Pico -> Additive Pico

Group (Additive CFloat)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive CFloat -> Additive CFloat

greplicate :: Integer -> Additive CFloat -> Additive CFloat

Group (Additive CDouble)

Defined in Data.Semigroup.Additive

Methods

inv :: Additive CDouble -> Additive CDouble

greplicate :: Integer -> Additive CDouble -> Additive CDouble

(Additive - Group) a => Group (Additive (V4 a))

Defined in Data.Semimodule.Vector

Methods

inv :: Additive (V4 a) -> Additive (V4 a)

greplicate :: Integer -> Additive (V4 a) -> Additive (V4 a)

(Additive - Group) a => Group (Additive (V3 a))

Defined in Data.Semimodule.Vector

Methods

inv :: Additive (V3 a) -> Additive (V3 a)

greplicate :: Integer -> Additive (V3 a) -> Additive (V3 a)

(Additive - Group) a => Group (Additive (V2 a))

Defined in Data.Semimodule.Vector

Methods

inv :: Additive (V2 a) -> Additive (V2 a)

greplicate :: Integer -> Additive (V2 a) -> Additive (V2 a)

(Additive - Group) a => Group (Additive (Quaternion a))

Defined in Data.Algebra.Quaternion

Methods

inv :: Additive (Quaternion a) -> Additive (Quaternion a)

greplicate :: Integer -> Additive (Quaternion a) -> Additive (Quaternion a)

Loop (Additive Double)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Double

lreplicate :: Natural -> Additive Double -> Additive Double

Loop (Additive Float)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Float

lreplicate :: Natural -> Additive Float -> Additive Float

Loop (Additive Int)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Int

lreplicate :: Natural -> Additive Int -> Additive Int

Loop (Additive Int8)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Int8

lreplicate :: Natural -> Additive Int8 -> Additive Int8

Loop (Additive Int16)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Int16

lreplicate :: Natural -> Additive Int16 -> Additive Int16

Loop (Additive Int32)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Int32

lreplicate :: Natural -> Additive Int32 -> Additive Int32

Loop (Additive Int64)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Int64

lreplicate :: Natural -> Additive Int64 -> Additive Int64

Loop (Additive Integer)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Integer

lreplicate :: Natural -> Additive Integer -> Additive Integer

((Additive - Group) a, (Multiplicative - Monoid) a) => Loop (Additive (Ratio a))

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive (Ratio a)

lreplicate :: Natural -> Additive (Ratio a) -> Additive (Ratio a)

Loop (Additive ())

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive ()

lreplicate :: Natural -> Additive () -> Additive ()

(Additive - Group) a => Loop (Additive (Complex a))

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive (Complex a)

lreplicate :: Natural -> Additive (Complex a) -> Additive (Complex a)

Loop (Additive Uni)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Uni

lreplicate :: Natural -> Additive Uni -> Additive Uni

Loop (Additive Deci)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Deci

lreplicate :: Natural -> Additive Deci -> Additive Deci

Loop (Additive Centi)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Centi

lreplicate :: Natural -> Additive Centi -> Additive Centi

Loop (Additive Milli)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Milli

lreplicate :: Natural -> Additive Milli -> Additive Milli

Loop (Additive Micro)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Micro

lreplicate :: Natural -> Additive Micro -> Additive Micro

Loop (Additive Nano)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Nano

lreplicate :: Natural -> Additive Nano -> Additive Nano

Loop (Additive Pico)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive Pico

lreplicate :: Natural -> Additive Pico -> Additive Pico

Loop (Additive CFloat)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive CFloat

lreplicate :: Natural -> Additive CFloat -> Additive CFloat

Loop (Additive CDouble)

Defined in Data.Semigroup.Additive

Methods

lempty :: Additive CDouble

lreplicate :: Natural -> Additive CDouble -> Additive CDouble

(Additive - Group) a => Loop (Additive (V4 a))

Defined in Data.Semimodule.Vector

Methods

lempty :: Additive (V4 a)

lreplicate :: Natural -> Additive (V4 a) -> Additive (V4 a)

(Additive - Group) a => Loop (Additive (V3 a))

Defined in Data.Semimodule.Vector

Methods

lempty :: Additive (V3 a)

lreplicate :: Natural -> Additive (V3 a) -> Additive (V3 a)

(Additive - Group) a => Loop (Additive (V2 a))

Defined in Data.Semimodule.Vector

Methods

lempty :: Additive (V2 a)

lreplicate :: Natural -> Additive (V2 a) -> Additive (V2 a)

(Additive - Group) a => Loop (Additive (Quaternion a))

Defined in Data.Algebra.Quaternion

Methods

lempty :: Additive (Quaternion a)

lreplicate :: Natural -> Additive (Quaternion a) -> Additive (Quaternion a)

Quasigroup (Additive Double)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Double -> Additive Double -> Additive Double

(\\) :: Additive Double -> Additive Double -> Additive Double

Quasigroup (Additive Float)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Float -> Additive Float -> Additive Float

(\\) :: Additive Float -> Additive Float -> Additive Float

Quasigroup (Additive Int)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Int -> Additive Int -> Additive Int

(\\) :: Additive Int -> Additive Int -> Additive Int

Quasigroup (Additive Int8)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Int8 -> Additive Int8 -> Additive Int8

(\\) :: Additive Int8 -> Additive Int8 -> Additive Int8

Quasigroup (Additive Int16)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Int16 -> Additive Int16 -> Additive Int16

(\\) :: Additive Int16 -> Additive Int16 -> Additive Int16

Quasigroup (Additive Int32)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Int32 -> Additive Int32 -> Additive Int32

(\\) :: Additive Int32 -> Additive Int32 -> Additive Int32

Quasigroup (Additive Int64)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Int64 -> Additive Int64 -> Additive Int64

(\\) :: Additive Int64 -> Additive Int64 -> Additive Int64

Quasigroup (Additive Integer)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Integer -> Additive Integer -> Additive Integer

(\\) :: Additive Integer -> Additive Integer -> Additive Integer

((Additive - Group) a, (Multiplicative - Monoid) a) => Quasigroup (Additive (Ratio a))

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive (Ratio a) -> Additive (Ratio a) -> Additive (Ratio a)

(\\) :: Additive (Ratio a) -> Additive (Ratio a) -> Additive (Ratio a)

Quasigroup (Additive ())

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive () -> Additive () -> Additive ()

(\\) :: Additive () -> Additive () -> Additive ()

(Additive - Group) a => Quasigroup (Additive (Complex a))

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive (Complex a) -> Additive (Complex a) -> Additive (Complex a)

(\\) :: Additive (Complex a) -> Additive (Complex a) -> Additive (Complex a)

Quasigroup (Additive Uni)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Uni -> Additive Uni -> Additive Uni

(\\) :: Additive Uni -> Additive Uni -> Additive Uni

Quasigroup (Additive Deci)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Deci -> Additive Deci -> Additive Deci

(\\) :: Additive Deci -> Additive Deci -> Additive Deci

Quasigroup (Additive Centi)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Centi -> Additive Centi -> Additive Centi

(\\) :: Additive Centi -> Additive Centi -> Additive Centi

Quasigroup (Additive Milli)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Milli -> Additive Milli -> Additive Milli

(\\) :: Additive Milli -> Additive Milli -> Additive Milli

Quasigroup (Additive Micro)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Micro -> Additive Micro -> Additive Micro

(\\) :: Additive Micro -> Additive Micro -> Additive Micro

Quasigroup (Additive Nano)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Nano -> Additive Nano -> Additive Nano

(\\) :: Additive Nano -> Additive Nano -> Additive Nano

Quasigroup (Additive Pico)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive Pico -> Additive Pico -> Additive Pico

(\\) :: Additive Pico -> Additive Pico -> Additive Pico

Quasigroup (Additive CFloat)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive CFloat -> Additive CFloat -> Additive CFloat

(\\) :: Additive CFloat -> Additive CFloat -> Additive CFloat

Quasigroup (Additive CDouble)

Defined in Data.Semigroup.Additive

Methods

(//) :: Additive CDouble -> Additive CDouble -> Additive CDouble

(\\) :: Additive CDouble -> Additive CDouble -> Additive CDouble

(Additive - Group) a => Quasigroup (Additive (V4 a))

Defined in Data.Semimodule.Vector

Methods

(//) :: Additive (V4 a) -> Additive (V4 a) -> Additive (V4 a)

(\\) :: Additive (V4 a) -> Additive (V4 a) -> Additive (V4 a)

(Additive - Group) a => Quasigroup (Additive (V3 a))

Defined in Data.Semimodule.Vector

Methods

(//) :: Additive (V3 a) -> Additive (V3 a) -> Additive (V3 a)

(\\) :: Additive (V3 a) -> Additive (V3 a) -> Additive (V3 a)

(Additive - Group) a => Quasigroup (Additive (V2 a))

Defined in Data.Semimodule.Vector

Methods

(//) :: Additive (V2 a) -> Additive (V2 a) -> Additive (V2 a)

(\\) :: Additive (V2 a) -> Additive (V2 a) -> Additive (V2 a)

(Additive - Group) a => Quasigroup (Additive (Quaternion a))

Defined in Data.Algebra.Quaternion

Methods

(//) :: Additive (Quaternion a) -> Additive (Quaternion a) -> Additive (Quaternion a)

(\\) :: Additive (Quaternion a) -> Additive (Quaternion a) -> Additive (Quaternion a)

Magma (Additive Double)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Double -> Additive Double -> Additive Double

Magma (Additive Float)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Float -> Additive Float -> Additive Float

Magma (Additive Int)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Int -> Additive Int -> Additive Int

Magma (Additive Int8)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Int8 -> Additive Int8 -> Additive Int8

Magma (Additive Int16)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Int16 -> Additive Int16 -> Additive Int16

Magma (Additive Int32)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Int32 -> Additive Int32 -> Additive Int32

Magma (Additive Int64)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Int64 -> Additive Int64 -> Additive Int64

Magma (Additive Integer)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Integer -> Additive Integer -> Additive Integer

((Additive - Group) a, (Multiplicative - Monoid) a) => Magma (Additive (Ratio a))

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive (Ratio a) -> Additive (Ratio a) -> Additive (Ratio a)

Magma (Additive ())

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive () -> Additive () -> Additive ()

(Additive - Group) a => Magma (Additive (Complex a))

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive (Complex a) -> Additive (Complex a) -> Additive (Complex a)

Magma (Additive Uni)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Uni -> Additive Uni -> Additive Uni

Magma (Additive Deci)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Deci -> Additive Deci -> Additive Deci

Magma (Additive Centi)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Centi -> Additive Centi -> Additive Centi

Magma (Additive Milli)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Milli -> Additive Milli -> Additive Milli

Magma (Additive Micro)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Micro -> Additive Micro -> Additive Micro

Magma (Additive Nano)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Nano -> Additive Nano -> Additive Nano

Magma (Additive Pico)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive Pico -> Additive Pico -> Additive Pico

Magma (Additive CFloat)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive CFloat -> Additive CFloat -> Additive CFloat

Magma (Additive CDouble)

Defined in Data.Semigroup.Additive

Methods

(<<) :: Additive CDouble -> Additive CDouble -> Additive CDouble

(Additive - Group) a => Magma (Additive (V4 a))

Matrix subtraction.

>>> V4 (V4 1 2 3) (V4 4 5 6) (V4 7 8 9) << V4 (V4 7 8 9) (V4 7 8 9) (V4 7 8 9)
V4 (V4 (-6) (-6) (-6)) (V4 (-3) (-3) (-3)) (V4 0 0 0)

Defined in Data.Semimodule.Vector

Methods

(<<) :: Additive (V4 a) -> Additive (V4 a) -> Additive (V4 a)

(Additive - Group) a => Magma (Additive (V3 a))

Matrix subtraction.

>>> V3 (V3 1 2 3) (V3 4 5 6) (V3 7 8 9) << V3 (V3 7 8 9) (V3 7 8 9) (V3 7 8 9)
V3 (V3 (-6) (-6) (-6)) (V3 (-3) (-3) (-3)) (V3 0 0 0)

Defined in Data.Semimodule.Vector

Methods

(<<) :: Additive (V3 a) -> Additive (V3 a) -> Additive (V3 a)

(Additive - Group) a => Magma (Additive (V2 a))

Matrix subtraction.

>>> m23 1 2 3 4 5 6 << m23 7 8 9 1 2 3 :: M23 Int
V2 (V3 (-6) (-6) (-6)) (V3 3 3 3)

Defined in Data.Semimodule.Vector

Methods

(<<) :: Additive (V2 a) -> Additive (V2 a) -> Additive (V2 a)

(Additive - Group) a => Magma (Additive (Quaternion a))

Defined in Data.Algebra.Quaternion

Methods

(<<) :: Additive (Quaternion a) -> Additive (Quaternion a) -> Additive (Quaternion a)

type Rep Additive

Defined in Data.Semigroup.Additive

type Rep Additive = ()

type Rep (Additive a)

Defined in Data.Semigroup.Additive

type Rep (Additive a) = D1 (MetaData "Additive" "Data.Semigroup.Additive" "rings-0.0.3-21Z3wlGnIMkBc1cJ09ZojY" True) (C1 (MetaCons "Additive" PrefixI True) (S1 (MetaSel (Just "unAdditive") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

Orphan instances

(Additive - Semigroup) a => Semigroup (Multiplicative [a])

Methods

(<>) :: Multiplicative [a] -> Multiplicative [a] -> Multiplicative [a]

sconcat :: NonEmpty (Multiplicative [a]) -> Multiplicative [a]

stimes :: Integral b => b -> Multiplicative [a] -> Multiplicative [a]

((Additive - Group) a, (Multiplicative - Semigroup) a) => Semigroup (Multiplicative (Complex a))

Methods

(<>) :: Multiplicative (Complex a) -> Multiplicative (Complex a) -> Multiplicative (Complex a)

sconcat :: NonEmpty (Multiplicative (Complex a)) -> Multiplicative (Complex a)

stimes :: Integral b => b -> Multiplicative (Complex a) -> Multiplicative (Complex a)

(Additive - Semigroup) a => Semigroup (Multiplicative (Min a))

Methods

(<>) :: Multiplicative (Min a) -> Multiplicative (Min a) -> Multiplicative (Min a)

sconcat :: NonEmpty (Multiplicative (Min a)) -> Multiplicative (Min a)

stimes :: Integral b => b -> Multiplicative (Min a) -> Multiplicative (Min a)

(Additive - Semigroup) a => Semigroup (Multiplicative (NonEmpty a))

Methods

(<>) :: Multiplicative (NonEmpty a) -> Multiplicative (NonEmpty a) -> Multiplicative (NonEmpty a)

sconcat :: NonEmpty (Multiplicative (NonEmpty a)) -> Multiplicative (NonEmpty a)

stimes :: Integral b => b -> Multiplicative (NonEmpty a) -> Multiplicative (NonEmpty a)

(Additive - Monoid) a => Monoid (Multiplicative [a])

Methods

mempty :: Multiplicative [a]

mappend :: Multiplicative [a] -> Multiplicative [a] -> Multiplicative [a]

mconcat :: [Multiplicative [a]] -> Multiplicative [a]

((Additive - Group) a, (Multiplicative - Monoid) a) => Monoid (Multiplicative (Complex a))

Methods

mempty :: Multiplicative (Complex a)

mappend :: Multiplicative (Complex a) -> Multiplicative (Complex a) -> Multiplicative (Complex a)

mconcat :: [Multiplicative (Complex a)] -> Multiplicative (Complex a)

(Additive - Monoid) a => Monoid (Multiplicative (Min a))

Methods

mempty :: Multiplicative (Min a)

mappend :: Multiplicative (Min a) -> Multiplicative (Min a) -> Multiplicative (Min a)

mconcat :: [Multiplicative (Min a)] -> Multiplicative (Min a)

((Additive - Group) a, (Multiplicative - Group) a) => Group (Multiplicative (Complex a))

Methods

inv :: Multiplicative (Complex a) -> Multiplicative (Complex a)

greplicate :: Integer -> Multiplicative (Complex a) -> Multiplicative (Complex a)

((Additive - Group) a, (Multiplicative - Group) a) => Loop (Multiplicative (Complex a))

Methods

lempty :: Multiplicative (Complex a)

lreplicate :: Natural -> Multiplicative (Complex a) -> Multiplicative (Complex a)

((Additive - Group) a, (Multiplicative - Group) a) => Quasigroup (Multiplicative (Complex a))

Methods

(//) :: Multiplicative (Complex a) -> Multiplicative (Complex a) -> Multiplicative (Complex a)

(\\) :: Multiplicative (Complex a) -> Multiplicative (Complex a) -> Multiplicative (Complex a)

((Additive - Group) a, (Multiplicative - Group) a) => Magma (Multiplicative (Complex a))

Methods

(<<) :: Multiplicative (Complex a) -> Multiplicative (Complex a) -> Multiplicative (Complex a)